The popularity of multimedia communications services over packet data networks, such as the Internet, continues to grow. Consequently, the demand for higher capacity in core data transport networks continues to grow. For service providers, core data transport networks are optical networks based on fiber optic technology. To increase the capacity of optical networks, advanced signal modulation techniques, such as quadrature amplitude modulation (QAM) and quadrature phase shift keying (QPSK) have been developed. The push for higher spectral efficiencies to lower the cost per transmitted bit and the concern about exhausting the fiber bandwidth has focused much recent research work on multi-level, multi-dimensional modulation formats to achieve the ultimate capacity in a single fiber.
Digital coherent detection has proven to be an effective technique for detecting and demodulating the received optical signals based on multi-level, multi-dimensional modulation formats. Although progress has been made, due to the increased optical-signal-to-noise ratio (OSNR) requirements, the reach of these multi-level, multi-dimensional modulation formats is clearly a concern. Thus, power efficient modulation formats, those having a low required signal-to-noise ratio per bit for a given bit-error-ratio, have also received attention, with significant focus on four-dimensional optimized formats (i.e. those using both quadratures and polarization components of the electromagnetic fields). Power-efficient modulation formats are of fundamental importance in optical communications because they provide the ultimate sensitivity limit for the optical channel. Such modulation formats also have practical importance because they enable increased nonlinear tolerance, and therefore the potential for ultra long-haul transmission.